Logics of Statements in Context – The Case of Many-Sorted
First-Order Logic
Logics of Statements in Context have been recently proposed as a
general framework to describe and relate, in a uniform and unifying
way, a broad spectrum of logics and specification formalisms which
also comprise “open formulas”. The concept of “statement in context”
is our novel proposal to formalize, in an adequate way, the rather
informal concept of “open formula”. In the talk we address the special
case of traditional Many-Sorted First-Order Logic. We discuss that any
many-sorted first-order signature Sigma with predicate and (!)
operation symbols gives rise to an institution FL(Sigma) of
Sigma-statements in context. As a methodological side-effect, we
provide some evidence that we are not fatefully doomed to formalize
variables by means of signature extensions when we do “abstract model
theory”!
At the end of the talk, we intend to outline the following
constructions and results: Assigning to each many-sorted first-order
signature Sigma the institution FL(Sigma) defines a functor from the
category of many-sorted signatures into the category of institutions
and comorphisms. We can construct a corresponding Grothendieck
institution FL# which turns out to be indeed a conservative extension
of the traditional institution of Many-Sorted First-Order Logic only
comprising “closed formulas”.
Uwe Wolter
Last modified: Tue Jun 10 2025